已知6x2-7xy-3y2+14x+y+a=(2x-3y+b)(3x+y+c),试确定a、b、c的值.

问题描述:

已知6x2-7xy-3y2+14x+y+a=(2x-3y+b)(3x+y+c),试确定a、b、c的值.

∵(2x-3y+b)(3x+y+c)=6x2-7xy-3y2+(2c+3b)x+(b-3c)y+bc∴6x2-7xy-3y2+(2c+3b)x+(b-3c)y+bc=6x2-7xy-3y2+14x+y+a∴2c+3b=14,b-3c=1,a=bc联立以上三式可得:a=4,b=4,c=1故a=4,b=4,c=1....